Unscented state estimation for rigid body attitude motion with a finite-time stable observer

Bohn, Jan; Sanyal, Amit K.; Butcher, Eric A.

doi:10.1109/cdc.2016.7798985

Cited by 8 publications

(6 citation statements)

References 22 publications

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“…Another line of research uses the unscented transform on Lie groups and Lie exponential coordinates to derive uncertainty ellipsoids that are proved to contain with certainty the state, when faced with bounded sensor errors, see [14,15]. [16,17] also introduced an Invariant UKF, as an UKF capable of taking into account the symmetries of the system's equations, for state spaces that are generally not Lie groups.…”

Section: A Links and Differences With Previous Literaturementioning

confidence: 99%

Unscented Kalman filtering on Lie groups

Brossard

Bonnabel

Condomines

2017

2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

101

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In this paper, we first consider a simple Bayesian fusion problem in a matrix Lie group, and propose to tackle it using the unscented transform. The method is then leveraged to derive two simple alternative unscented Kalman filters on Lie groups, for both cases of noisy partial measurements of the state, and full state noisy measurements of the state on the group. The general method is applied to a robot localization problem, and results based on experimental data combined with extensive Monte-Carlo simulations at various noise levels illustrate the superiority of the approach over the standard UKF.

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Section: A Links and Differences With Previous Literaturementioning

confidence: 99%

Unscented Kalman filtering on Lie groups

Brossard

Bonnabel

Condomines

2017

2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

101

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“…In the first step, the relative attitude Q is determined based on the relation (4), by a solution of Wahba's problem on SO(3). In the second step, relative translational velocityṗ O and relative angular velocity Υ of frame O as observed from frame S, are obtained using expression (12).…”

Section: Determination Of Relative Motionmentioning

confidence: 99%

“…This state determination problem is based on the relation (12). Letṗ m O and Υ m denote the instantaneous relative velocities determined from measurements ofṗ O and Υ respectively, and define…”

Section: B Velocity Determination From Range and Range Rate Measuremmentioning

confidence: 99%

“…For determination of these relative velocities, the sensors need to satisfy a few conditions on their line-of-sight directions and their locations on the observing body. This instantaneous relative motion determination scheme can be used in conjunction with an observer or estimator designed on the Lie group of rigid body motions, SE(3) ((e.g., [12], [13]), for dynamic estimation of relative motion states.…”

Section: Introductionmentioning

confidence: 99%

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Determination of relative motion of a space object from simultaneous measurements of range and range rate

Sanyal

Izadi

Butcher

2014

2014 American Control Conference

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This tutorial paper considers determination of instantaneous relative motion of a space object, from line-of-sight range and range rate measurements made by sensors fixed to a spacecraft in its proximity. Practical applications of this relative motion determination problem include uncooperative rendezvous prior to docking between space vehicles, capture of out-of-control spacecraft, capture of space debris and asteroids, locating and determining the attitude of space objects, and proximity operations near asteroids and comets. It is shown that the relative attitude of the space object with respect to the observing spacecraft can be determined from line-ofsight range measurements to at least three points on the object being observed, which requires three lidar or radar Doppler sensors. Determining the instantaneous relative translational and angular velocities of the space object also requires range and range rate measurements for at least three distinct points on the object, provided that certain conditions on the locations of the corresponding sensors and directions of their lines of sight are met.

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“…the Levi-Civita connection but mastering differential geometry is difficult. [7,13,20,21] are reserved for SO (3) and SE(3), while [23] is reserved for Lie groups and requires more knowledge of Lie theory than the present paper.…”

Section: Introductionmentioning

confidence: 99%

A Code for Unscented Kalman Filtering on Manifolds (UKF-M)

Brossard

Barrau

Bonnabel

2020

2020 IEEE International Conference on Robotics and Automation (ICRA)

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The present paper introduces a novel methodology for Unscented Kalman Filtering (UKF) on manifolds that extends previous work by the authors on UKF on Lie groups. Beyond filtering performance, the main interests of the approach are its versatility, as the method applies to numerous state estimation problems, and its simplicity of implementation for practitioners not being necessarily familiar with manifolds and Lie groups. We have developed the method on two independent open-source Python and Matlab frameworks we call UKF-M, for quickly implementing and testing the approach. The online repositories contain tutorials, documentation, and various relevant robotics examples that the user can readily reproduce and then adapt, for fast prototyping and benchmarking. The code is available at

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Unscented state estimation for rigid body attitude motion with a finite-time stable observer

Cited by 8 publications

References 22 publications

Unscented Kalman filtering on Lie groups

Unscented Kalman filtering on Lie groups

Determination of relative motion of a space object from simultaneous measurements of range and range rate

A Code for Unscented Kalman Filtering on Manifolds (UKF-M)

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